|
|
| MAKL5760 | Advanced Numerical Methods in Engineering | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MECHANICAL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | No | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to give students the basics for modeling and advanced numerical methods for analysing engineering systems. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn basics of mathematical modeling for engineering systems, | 1,5,8 | 1,3 | | PO - 2 : | learn solution techniques for lineer ve non-lineer algebraic equations and equation systems, and choose appropriate method for their specific problems, | 1,5,9 | 1,3 | | PO - 3 : | aplly single-step, constant step-size and adaptive-step size, RungeKutta methods to solve ODEs and ODE systems, | 1,5,9 | 1,3 | | PO - 4 : | apply implicit and multi-step methods to solve stiff systems, | 1,5,9 | 1,3 | | PO - 5 : | learn solution techniques for boundary-value and eigen-value problems, | 1,5,9 | 1,3 | | PO - 6 : | apply learned numerical techniques by using MATLAB programming language. | 1,5,11 | 1,3 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Mathematical modeling of engineering systems. Solution of linear and non-linear algebraic equations and equation systems. Single-step (Runge-Kutta) methods for solving ODEs and ODE systems. Stiffness and multi-step methods. Boundary-value and eigen-value problems in engineering and solution methods. Numerical solutions of partial differential equations. MATLAB applications of solutions. |
| |
| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Motivation. Mathematical modeling, numerical methods and engineering practice. | | | Week 2 | Direct solution methods used for lineer ve non-lineer algebraic equations and equation systems. | | | Week 3 | Iterative solution methods used for lineer ve non-lineer algebraic equations and equation systems. | | | Week 4 | Fixed step-size, single-step methods applied for solving ordinary differential equations (ODEs) and equation systems. | | | Week 5 | Adaptive step-size single-step methods applied for solving ODEs and equation systems. | | | Week 6 | Error control and Runge-Kutta Fehlberg method. | | | Week 7 | Stiffness and stiff ODEs and equation systems. Explicit and implicit methods. | | | Week 8 | Multistep methods. Non-self-starting Heun Method. | | | Week 9 | Mid-term exam | | | Week 10 | Higher-order multi-step methods. | | | Week 11 | General methods applied for solution of boundary value problems. Shooting methods for linear and non-linear problems. | | | Week 12 | Finite-difference methods for boundary value problems. | | | Week 13 | Eigen value and the solutions of eigen value problems. | | | Week 14 | The methods applied for the partial differential equations (PDE): Elliptic equations and finite difference methods. | | | Week 15 | PDEs and finite-volume approaches. | | | Week 16 | End-of-term exam | | | |
| 1 | Chapra, SC. , Applied Numerical Methods with MATLAB for Engineers and Scientists, Third Edition, McGraw-Hill, New York. (ISBN 978-0-07-340110-2) | | | |
| 1 | Chapra, SC., Canale, RP. 1998; Numerical Methods for Engineers, 3rd Ed., McGraw-Hill, New York. (ISBN 0-07-010938-9) | | | 2 | Mathews, JH., Fink, KD. 1999; Numerical Methods Using MATLAB, 3rd Ed., Prentice-Hall, New York. (ISBN 0-13-270042-5). | | | 3 | Burden, RL., Faires, JD. 2005; Numerical Analysis, 8th Ed., Thomson, Belmont USA. (ISBN 0-534-40499-5). | | | 4 | serles, A. 2009; A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, UK. (ISBN 978-0-521-73490-5). | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 20/11/2018 | 2 | 30 | | Homework/Assignment/Term-paper | 13 | 18/12/2018 | 2 | 20 | | End-of-term exam | 17 | 15/01/2019 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 3 | 5 | 15 | | Arasınav | 2 | 1 | 2 | | Uygulama | 1 | 7 | 7 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 4 | 7 | 28 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 3 | 5 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 3 | 5 | 15 | | Diğer 2 | 3 | 5 | 15 | | Total work load | | | 197 |
|